An empirical examination of risk equalisation in a regulated community rated health insurance market

Despite universal access entitlements to the public healthcare system in Ireland, over half the population is covered by voluntary private health insurance. The market operates on the basis of community rating, open enrolment and lifetime cover. A set of minimum benefits also exists, and two risk equalisation schemes have been put in place but neither was implemented. These schemes have proved highly controversial. To date, the debate has primarily consisted of qualitative arguments. This study adds a quantitative element by analysing a number of pertinent issues. A model of a community rated insurance market is developed, which shows that community rating can only be maintained in a competitive market if all insurers in the market have the same risk profile as the market overall. This has relevance to the Irish market in the aftermath of a Supreme Court decision to set aside risk equalisation. Two reasons why insurers’ risk profiles might differ are adverse selection and risk selection. Evidence is found of the existence of both forms of selection in the Irish market. A move from single rate community rating to lifetime community rating in Australia had significant consequences for take-up rates and the age profile of the insured population. A similar move has been proposed in Ireland. It is found that, although this might improve the stability of community rating in the short term, it would not negate the need for risk equalisation. If community rating were to collapse then risk rating might result. A comparison of the Irish, Australian and UK health insurance markets suggests that community rating encourages higher take-up among older consumers than risk rating. Analysis of Irish hospital discharge figures suggests that this yields significant savings for the Irish public healthcare system. This thesis has implications for government policy towards private health insurance in Ireland.

Financial modelling with 2-EPT probability density functions

The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.

Characterization of TRAF6 mediated ubiquitination of presenilins and γ-secretase substrates

Post-translational modification of the γ-secretase protease complexes and their substrates has an important role in controlling receptor-initiated signalling events, which are critically important in the pathogenesis of cancer, inflammatory and Alzheimer’s disease. Our lab has previously characterised an interaction between TRAF6 and presenilin-1, which lead to the identification of interleukin-1 (IL-1) receptor type 1 (IL-1R1) and Toll-like receptor-4 (TLR4) as novel γ-secretase substrates. Subsequently our group showed that TRAF6 promoted ubiquitination and γ-secretase cleavage of IL-1R1. The aim of this project is to study the association between TRAF6 and the presenilins, the critical γ-secretase complex components, and to determine the functional importance of TRAF6-mediated ubiquitination of γ-secretase substrates. Firstly, we show that the full-length presenilins are novel substrates of TRAF6-mediated Lysine-63-linked polyubiquitination. Secondly, we show that co-expression of TRAF6 and the presenilins increases the stability and alters the turnover of the presenilins. Thirdly, we reveal that TRAF6-mediated ubiquitination of presenilin does not affect γ-secretase enzyme activity, but may regulate the full-length presenilin functions such as ER Ca2+ signalling. Previously, we have reported IL-1R1 as a novel substrate of TRAF6-mediated ubiquitination. In this study, we identified five lysine residues in the IL-1R1 intracellular domain targeted by TRAF6-mediated polyubiquitination. Furthermore, mutagenesis of these five lysine residues led to decreased IL-1R1 cell surface expression, precluded the ectodomain shedding and attenuated the responsiveness to IL-1β stimulation, demonstrating the critical role of TRAF6 in IL-1R1 trafficking.

The Rpf/DSF system and the regulation of virulence in the plant pathogen Xanthomonas campestris

The full virulence of Xanthomonas campestris pv. campestris (Xcc) to plants depends upon cell-to-cell signalling mediated by the signal molecule DSF (for diffusible signal factor), that has been characterised as cis-11-methyl-2-dodecenoic acid. DSF-mediated signalling regulates motility, biofilm dynamics and the synthesis of particular virulence determinants. The synthesis and perception of the DSF signal molecule involves products of the rpf (regulation of pathogenicity factors) gene cluster. DSF synthesis is fully dependent on RpfF, which encodes a putative enoyl-CoA hydratase. A two-component system, comprising the complex sensor histidine kinase RpfC and the HD-GYP domain regulator RpfG, is implicated in DSF perception. The HD-GYP domain of RpfG is a phosphodiesterase working on cyclic di-GMP; DSF perception is thereby linked to the turnover of this intracellular second messenger. The full range of regulatory influences of the Rpf/DSF system and of cyclic di-GMP in Xcc has yet to be established. In order to further characterise the Rpf/DSF regulatory network in Xcc, a proteomic approach was used to compare protein expression in the wildtype and defined rpf mutants. This work shows that the Rpf/DSF system regulates a range of biological functions that are associated with virulence and biofilm formation but also reveals new functions mediated by DSF regulation. These functions include antibiotic resistance, detoxification and stress tolerance. Mutational analysis showed that several of these regulated protein functions contribute to virulence in Chinese radish. Interestingly, it was demonstrated that different patterns of protein expression are associated with mutations of rpfF, rpfC and rpfG. This suggests that RpfG and RpfC have broader roles in regulation other than perception and transduction of DSF. Taken together, this analysis indicates the broad and complex regulatory role of Rpf/DSF system and identifies a number of new functions under Rpf/DSF control, which were shown to play a role in virulence.